Summary: We discuss the results of a fourth-order spectro-consistent discretization of incompressible Navier-Stokes equations. In such an approach, the discretization of a (skew-)symmetric operator is given by a (skew-)symmetric matrix. We present numerical experiments with spectro-consistent discretizations and traditional methods for a one-dimensional convection-diffusion equation. LES and Reynolds-averaged Navier-Stokes (RANS) simulations are challenged by giving a number of examples for which a fourth-order, spectro-consistent discretization of the Navier-Stokes equations without any turbulence model yields better (or at least equally good) results as large-eddy simulations or RANS computations, whereas the grids are comparable. The examples are taken from a number of recent workshops on complex turbulent flows.